Basic Rook Endgames

We lost on board count to old rivals Teignmouth in the Peter Rooke Cup
at the end of January. One of the last games to finish involved a
simple-looking Rook endgame. Just as it was getting crucial, White,
short of time, found a time-saving blunder:

So what should the result have been? I discussed it briefly with my
friend Bill Ingham. As is often the way, he fancied his side's chances
to win, and I hoped for a draw, but the discussion showed how vague we
all are about some basic theory. To be fair, some apparently small
differences can change the best obtainable result:

Before I answer that, I want to decide: regardless of the right result,
what is the right approach?

You probably know the Philidor and Lucena positions. Philidor showed a
draw, with the defending King having control of the Queening square. The
defender keeps out the attacking King. White can make progress only by
pushing the pawn, the Black shows a draw by sending the Rook a long way
away and playing a flurry of checks.

{ Black K has control of the queening square and bR has control of the sixth}
1. Kf5 1... Rc6 {
now there is no shelter on the board from the checks for the White King.} 2. e6
Rc1 3. Kf6 Rf1+ 4. Ke5 Re1+ 5. Kd4 Rd1+ 6. Ke4 Re1+ 7. Kd5 1/2-1/2

The 'Lucena' position, shown by Salvio and attributed to Sciapino, is a
win for the attacking side. With the defending King cut off by at least
two files, the defending Rook has to play the flurry of checks from
across the board. The attacker either makes an escape hatch for the
King, or 'builds a bridge' so that the Rook can step in at the right
moment.

Eagle-eyed readers will have spotted that I cheated: I swapped around
the Rooks, giving the defender one more file's-worth of checking
distance. In a position like the actual game, with the defending Rook on
the b-file, it's not quite enough:

Now, when Bill and I were playing around with this position, I managed
to persuade him that it might be a draw, because he couldn't escape the
flurry of checks, because he didn't approach the Rook with his King. I
didn't know the theoretical result, but I did know the best thing to
try.

It's very well worth your while to play out these positions against a
friend or a computer, so that if and when it turns up in one of your
games, you won't hesitate to adopt the right approach.